The marked price of an article is Rs. 1500. A shopkeeper sells it by giving 20% discount on its marked price. If the cost price of the article is Rs. 991, then his profit (in Rs.) is:
209
Calculating Profit with Discount on Marked Price
This problem involves calculating the profit made by a shopkeeper after selling an article at a discount on its marked price, given the cost price.
Understanding Key Terms: Marked Price, Discount, Selling Price, Cost Price, Profit
- Marked Price (MP): The price printed on the article or tagged on it. This is often the initial price before any discounts. In this case, the marked price is Rs. 1500.
- Discount: A reduction in the marked price, usually expressed as a percentage. Here, a 20% discount is given.
- Selling Price (SP): The actual price at which the article is sold after applying the discount.
- Cost Price (CP): The price at which the shopkeeper bought the article. The cost price is Rs. 991.
- Profit: The gain made by the shopkeeper when the selling price is greater than the cost price. Profit = Selling Price - Cost Price.
Step-by-Step Profit Calculation
Step 1: Calculate the Discount Amount
The shopkeeper gives a 20% discount on the marked price of Rs. 1500.
Discount amount = 20% of Marked Price
Discount amount $= \frac{20}{100} \times 1500$
Discount amount $= 0.20 \times 1500$
Discount amount $= 300$
The discount amount is Rs. 300.
Step 2: Calculate the Selling Price (SP)
The selling price is the marked price minus the discount amount.
Selling Price = Marked Price - Discount Amount
Selling Price $= 1500 - 300$
Selling Price $= 1200$
The article is sold for Rs. 1200.
Step 3: Calculate the Profit
The cost price of the article is given as Rs. 991. Profit is the difference between the selling price and the cost price.
Profit = Selling Price - Cost Price
Profit $= 1200 - 991$
Profit $= 209$
The profit made by the shopkeeper is Rs. 209.
Let's summarize the calculations:
| Item | Value (Rs.) |
|---|---|
| Marked Price (MP) | 1500 |
| Discount Percentage | 20% |
| Discount Amount ($20\%$ of $1500$) | 300 |
| Selling Price (SP = MP - Discount) | $1500 - 300 = 1200$ |
| Cost Price (CP) | 991 |
| Profit (SP - CP) | $1200 - 991 = 209$ |
Based on the calculations, the profit made by the shopkeeper is Rs. 209.
Revision Table: Important Concepts for Profit and Loss
| Concept | Formula | Notes |
|---|---|---|
| Discount | Discount % of Marked Price | Reduction from Marked Price |
| Selling Price (with Discount) | Marked Price - Discount Amount | Actual price paid by customer |
| Profit | Selling Price - Cost Price | Occurs when SP > CP |
| Loss | Cost Price - Selling Price | Occurs when CP > SP |
| Profit Percentage | $\left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100\%$ | Calculated on Cost Price |
| Loss Percentage | $\left(\frac{\text{Loss}}{\text{Cost Price}}\right) \times 100\%$ | Calculated on Cost Price |
Additional Information on Profit and Loss Problems
Profit and loss concepts are fundamental in commercial mathematics. They help us understand the financial outcome of buying and selling transactions. When dealing with discounts, it's important to remember that the discount is typically calculated on the marked price, while profit or loss is calculated based on the cost price and the selling price.
Sometimes, questions might involve successive discounts or include sales tax, which would further affect the final selling price. Always read the problem carefully to identify all factors influencing the transaction.
Important Questions from Discount and MP
Surbhi sold an article for Rs. 176 after giving 12% discount on its marked price. Had she not given any discount; she would have earned a profit of 25%. What is the cost price (in Rs.) of the article?
The marked price of an article is Rs. 240. A shopkeeper sells it by allowing 18% discount on its marked price and still gains 23%. What is the cost price (in Rs.) of the article?
Three shopkeepers A, B and C marked on an identical article at Rs. 4820. A, B and C sold their article on successive discounts of 20% and 20%; 25% and 15%; 30% and 10% respectively. Which shopkeeper gives the maximum discount and how much (in Rs.)?
Find a single discount percentage equivalent to successive discounts of 10%, 20% and 25%.
A shopkeeper marks the price of the article in such a way that after allowing 28% discount, he wants a gain of 12%. If the marked price is Rs. 224, then the cost price of the article is:
